Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $7062.5
Rate of Simple Interest (R) = 5%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$7062.5 = P (1 + 5% × 5)
⇒ $7062.5 = P (1 + 5/100 × 5)
⇒ $7062.5 = P (1 + 5 × 5/100)
⇒ $7062.5 = P (1 + 25/100)
⇒ $7062.5 = P (100 + 25/100)
⇒ $7062.5 = P × 125/100
⇒ P × 125/100 = $7062.5
⇒ P = 7062.5/125/100
⇒ P = 7062.5 × 100/125
⇒ P = 7062.5 × 100/125
⇒ P = 706250/125
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7062.5, then the Principal = 100/125 × 7062.5
= 100 × 7062.5/125
= 706250/125
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.